Final answer:
The rough endoplasmic reticulum is the organelle responsible for the synthesis of proteins by bound ribosomes, and it works closely with the Golgi apparatus, which modifies and packages these proteins.
Step-by-step explanation:
The organelle responsible for the synthesis of proteins by bound ribosomes is the rough endoplasmic reticulum (RER). The RER is studded with ribosomes on its membrane, which give it a distinctive rough appearance. These ribosomes are the site of protein synthesis, where they produce proteins that are then transported within the cell or may be exported outside the cell. In contrast, the smooth endoplasmic reticulum (SER) lacks ribosomes and is involved in lipid synthesis. The Golgi apparatus comes into play after the rough ER, where it further modifies, organizes, and packages these proteins into vesicles. It is important to note that the proteasome is not involved in the synthesis of proteins; it is involved in the degradation of proteins.